Algebraic & Geometric Topology

Units of equivariant ring spectra

Rekha Santhanam

Full-text: Open access

Abstract

It is well known that very special Γ–spaces and grouplike E–spaces both model connective spectra. Both these models have equivariant analogues in the case when the group acting is finite. Shimakawa defined the category of equivariant Γ–spaces and showed that special equivariant Γ–spaces determine positive equivariant spectra. Costenoble and Waner [Trans. Amer. Math. Soc. 326 (1991) 485-505] showed that grouplike equivariant E–spaces determine connective equivariant spectra.

We show that with suitable model category structures the category of equivariant Γ–spaces is Quillen equivalent to the category of equivariant E–spaces. We define the units of equivariant ring spectra in terms of equivariant Γ–spaces and show that the units of an equivariant ring spectrum determines a connective equivariant spectrum.

Article information

Source
Algebr. Geom. Topol., Volume 11, Number 3 (2011), 1361-1403.

Dates
Received: 27 December 2009
Revised: 1 February 2011
Accepted: 21 February 2011
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715231

Digital Object Identifier
doi:10.2140/agt.2011.11.1361

Mathematical Reviews number (MathSciNet)
MR2821427

Zentralblatt MATH identifier
1227.55014

Subjects
Primary: 55P91: Equivariant homotopy theory [See also 19L47] 55P42: Stable homotopy theory, spectra
Secondary: 55P47: Infinite loop spaces 55P48: Loop space machines, operads [See also 18D50]

Keywords
equivariant infinite loop space equivariant $\Gamma$–space equivariant spectra

Citation

Santhanam, Rekha. Units of equivariant ring spectra. Algebr. Geom. Topol. 11 (2011), no. 3, 1361--1403. doi:10.2140/agt.2011.11.1361. https://projecteuclid.org/euclid.agt/1513715231


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